Question 385495: In Dallas, some fire trucks were painted yellow (instead of red) to heighten their visibility. During
a test period, the fleet of red fire trucks made 153,348 runs and had 20 accidents, while the fleet of
yellow fire trucks made 135,035 runs and had 4 accidents. At α = .01, did the yellow fire trucks
have a significantly lower accident rate? (a) State the hypotheses. (b) State the decision rule and
sketch it. (c) Find the sample proportions and z test statistic. (d) Make a decision. (e) Find the
p-value and interpret it. (f ) If statistically significant, do you think the difference is large enough to
be important? If so, to whom, and why? (g) Is the normality assumption fulfilled? Explain.
My question is...I don't know where to start. How do I know what formula to use? To find the z value, excel wants variable ranges. ?? How do I find the sample proportions?
I am in a crunch situation and need the answers, but I also want to know how to do the problems.
Thanks
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In Dallas, some fire trucks were painted yellow (instead of red) to heighten their visibility. During a test period, the fleet of red fire trucks made 153,348 runs and had 20 accidents,
p-hat(red) = 20/153,348 = 0.0001304
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while the fleet of yellow fire trucks made 135,035 runs and had 4 accidents.
p-hat(yellow) = 4/135,035 = 0.00002962
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Difference of sample proportions: 0.0001006
At α = .01, did the yellow fire trucks have a significantly lower accident rate?
(a) State the hypotheses.
Ho: p(red) - p(yellow) =0
Ha: p(red) - p(yellow) > 0
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(b) State the decision rule and sketch it.
Reject Ho is z > 2.326
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(c) Find the sample proportions and z test statistic.
Using a TI calculator for a 2-Proportion Z-Test I get
z = 2.961
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(d) Make a decision.
Reject Ho
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(e) Find the p-value and interpret it.
P(z>2.961) = 0.0015..
0.015% of test results could have given stronger evidence for rejecting Ho.
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(f ) If statistically significant, do you think the difference is large enough to be important? If so, to whom, and why?
I'll leave that to you.
Looks like yellow wins.
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(g) Is the normality assumption fulfilled? Explain
Independence and x < 10%
I'll leave that to you.
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Cheers,
Stan H.
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